The Chandrasekhar-Dirac (CD) [1]} equations in Newman-Penrose formalism are given
by
\(\left( D+\epsilon -\rho \right) F_{1}+\left( \bar{\delta }+\pi -\alpha \right) F_{2} &=&0, \\\left( \nabla +\mu -\gamma \right) F_{2}+\left( \delta +\beta -\tau \right)F_{1} &=&0, \\\left( D+\bar{\epsilon }-\bar{\rho }\right) G_{2}-\left( \delta +\bar{\pi }-\bar{\alpha }\right) G_{1} &=&0, \\\left( \nabla +\bar{\mu }-\bar{\gamma }\right) G_{1}-\left( \bar{\delta }+\bar{\beta }-\bar{\tau }\right) G_{2} &=&0, \) 
